When travelling from Arica in Chile, taxi drivers will be patrolling teh international terminal to try and fill their taxis.
Buses don't really cross it and you have to take a taxi collectivo i.e a taxi that will leave when it is full (usually 5 passengers) from the international terminal in Tacna. These taxis are very, very old, most are old cadillac or similar from the 50s!!!! Very fun though.
The journey will take approx an hour. You will have to get off at the border, do the formalities and go back in your cab.
When I arrived in Tacna our intention was to be dropped at the bus terminal to take a 7 or 8 hour bus to Arequipa. Our taxi driver however told us that a flight would only take 30 minutes and would cost 25 US dollars (bus was 12 US dollars). We went to the AeroCondor office in Tacna and because of the time of year we actually paid 40 US dollars but I think it was definitely worth it!
If you want to go from Arica to Tacna in Peru the most convenient way is to take a colectivo taxi. We were able to negotiate one from the airport without having to go into town. All you need is four passengers who are wanting to cross over and away you go. It cost us 5000 pesos each for the fare and the taxi driver helped us with all the paperwork through the border.